The term in logic for the means by which the second operation of the intellect (i.e., judgment) is attained. More precisely, it is the affirmation or negation of a predicate of a subject.  Sometimes a distinction is drawn between a statement (when referring solely to the activity of the second operation of the intellect) and a proposition (when referring to the statements used in discursive reasoning). 

Categorical Proposition (also called Simple Proposition).— A proposition composed of a single subject and a single predicate. E.g., “Elephants are mammals.” 

Compound Proposition (also called Hypothetical Proposition).— A proposition composed of two or more categorical propositions. 

Conditional Proposition.— A compound proposition whose propositions are joined by an If…then. E.g., “If the weather is poor, then it is unpleasant.” The proposition that precedes the “then” is called the “antecedent” and the one that follows the “then” is called the “consequent.” If the antecedent is true, then the consequent must be true but not vice-versa (modus ponens). If the antecedent is false, then the truth value of the consequent is unknown. If the consequent is false, then the antecedent must be false (modus tollens). 

Conjunctive Proposition.— A compound proposition whose propositions are joined by an and. E.g., “The train will come from Milan, and it will arrive on time.” The propositions of a conjunctive proposition are called “conjuncts.” For an affirmative conjunctive proposition to be true, both conjuncts must be true. For a negative conjunctive proposition to be true, at least one conjunct must be false. 

Disjunctive Proposition.— A compound proposition whose propositions are joined by an or. E.g., “The economy is strong, or it is weak.” The propositions of a disjunctive proposition are called “disjuncts.” 

Strong Disjunctive Proposition.— A disjunctive proposition in which one of the disjuncts must be true but both cannot be true. Thus, if one is true, the other must be false and vice-versa. E.g., “The economy is strong, or it is weak.”  This kind of disjunctive proposition is also referred to as an “exclusive OR”. 

Weak Disjunctive Proposition.— A disjunctive proposition in which at least one of the disjuncts must be true and possibly both are true. Thus, if one is false, the other must be true but not vice-versa. E.g., “The professor was drunk, or he was insane.”  This kind of disjunctive proposition is also referred to as an “inclusive OR”.